Class Numbers via 3-Isogenies and Elliptic Surfaces

Details Class Numbers via 3-Isogenies and Elliptic Surfaces Class Numbers via 3-Isogenies and Elliptic Surfaces

2012-03-15

arxiv.org/abs/1203.3560v1

Mathematics

Number Theory

12 pages

Scientific paper

We show that a character sum attached to a family of 3-isogenies defined on
the fibers of a certain elliptic surface over $\mathbb{F}_p$ relates to the
class number of the quadratic imaginary number field $\Q(\sqrt{-p})$. In this
sense, this provides a higher-dimensional analog of some recent class number
formulas associated to 2-isogenies of elliptic curves.

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